In this case you need to two factors (x+ a) and (x+ d). First, you have to look for the factor of c, that c= (a)(d), and b must be a + d.
In this example, c= 6. Which are the factors of 6? 6*1 and 3*2
Now, you can verify: c= 6*1=6; b= 6+1= 7. IN this case 6 and 1 could not be the factors of x²+5x+6 because 6+1= 7, and not 5.
In the other hand, c= 3*2=6; b= 3+2=5
Now you can factorize x² + 5x + 6 = (x+3) (x+2).
ax² + bx + c
First, you have to look for the factors of a and c to know which one will be in th b value:
example: 7x² + 9x + 2
Factor of 7x²= 7x * x; factors of 2: 2 * 1
now, you can do the following:
7x + 1
x + 2 and use cross multiplication and sum the results (which can give you the value of bx).
(7x)*(2)= 14 x; (x)*1 = x; 14x + x= 15x. If we notice, b is 9, so, this are not the factors for that polynomial. If you have no the correct answer, you must switch the factors:
Answers & Comments
x² + bx + c
example: x² + 5x+6
In this case you need to two factors (x+ a) and (x+ d). First, you have to look for the factor of c, that c= (a)(d), and b must be a + d.
In this example, c= 6. Which are the factors of 6? 6*1 and 3*2
Now, you can verify: c= 6*1=6; b= 6+1= 7. IN this case 6 and 1 could not be the factors of x²+5x+6 because 6+1= 7, and not 5.
In the other hand, c= 3*2=6; b= 3+2=5
Now you can factorize x² + 5x + 6 = (x+3) (x+2).
ax² + bx + c
First, you have to look for the factors of a and c to know which one will be in th b value:
example: 7x² + 9x + 2
Factor of 7x²= 7x * x; factors of 2: 2 * 1
now, you can do the following:
7x + 1
x + 2 and use cross multiplication and sum the results (which can give you the value of bx).
(7x)*(2)= 14 x; (x)*1 = x; 14x + x= 15x. If we notice, b is 9, so, this are not the factors for that polynomial. If you have no the correct answer, you must switch the factors:
7x + 2
x + 1 and make the cross multiplication:
(7x)*1= 7x ; (x)*2 = 2x ; 7x + 2x= 9x
Now you have found the correct answer:
7x² + 9x + 2 = (7x+2) (x+1).
I Hope It Can Help!!